International Journal of Computer Architecture and ... of two binary m-sequence. III. RNS Based PN...
Transcript of International Journal of Computer Architecture and ... of two binary m-sequence. III. RNS Based PN...
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
Available Online at: www.ijcam.com
RNS Based Pn Sequence code in WCDMA and DSCDMA Sourabh Gupta
1 & Prof. Girish Tiwari
2
Department Of Electronics And Communication Engineering, Ujjain Engineering College, Ujjain M.P. (India)
[email protected] 1 , [email protected]
2
Abstract : Code Division Multiple Access
(CDMA) based on Spread Signal (SS) has
emerged as one of the most important multiple
access technologies for Second Generation (2G)
and Third Generation (3G) wireless
communication systems by its wide applications
in many important mobile cellular standards.
CDMA technique relies on spreading codes to
separate different users or channels and its
properties will govern the performance of the
system. It is known that orthogonal Codes are used to
multiplex more than one signal for downlink
transmission over cellular networks. This
downlink transmission is prone to self
interference caused by the loss of orthogonality
between spreading codes due to multipath
propagation. This issue is investigated in detail
with respect to WCDMA standards, which is
very good representative for CDMA based 3G
mobile cellular systems where the
channelization code is OVSF code. The problem
of OVSF codes restricts the number of available
codes for a given cell. Since the 3rd
generation
WCDMA mobile communication systems apply
the same multiple access technique, the
generated sequence can also be the
channelization code for downlink WCDMA
system to mitigate the same. The performance of
the system is compared with Walsh Hadamard
code over multipath AWGN and different
Fading channels. This thesis work shows that
RNS based PN sequence has enhanced
performance to that of other CDMA codes by
comparing the bit error probability in multiuser
and multipath environment thus contributing a
little towards the evolution of next generation
CDMA technology.
Keywords : RNS, CDMA,2G,3G,PN
sequence, WCDMA
I.Introduction
Residue number systems are based on the
congruence relation as: two integers, a and b are
said to be congruent modulo m if m divides
exactly the difference of a and b; it is common,
especially in mathematics tests, to write
a ≡ b mod m to denote this. Thus, for
example, 10 ≡ 7(mod 3), 10 ≡ 4(mod 3), 10 ≡
1(mod 3) and 10 ≡ 2(mod 3). The number m is
a modulus or base, and its values exclude unity
produces only trivial congruence’s [26, 27].
If q and r are the quotient and remainder,
respectively, of the integer division of a by m
i.e. a = q ∗ m + r,
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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Then, by definition a≡ r (mod m).The number r
is said to be the residue of a with respect to m,
and is denoted by r = a m.
As an example, the residues of the integers zero
through fifteen relative to the module two, three
and five (which are pair wise relative prime) are
given in the left half of Table 2.1. And the
residues of the same numbers relative to the
module two, three and four (which are pair wise
relatively prime) are given in the right half of the
same table. Observe that no sequence of residues
is repeated in the first half, whereas there are
repetitions in the second.
The set of m smallest values,{0,1,2,3…(m-1)}
that the residue may assume is called the set of
least positive residue modulo m. Consider a set
{m1,m2,…mn },of n positive and pair wise
relatively prime module. Let R be the product of
the module for every j and k if j ≠ k, then mj
and mk have no common divisor larger than
unity. Then every number X< R has unique
representation in the residue number system
[26,27]. A partial proof of this is as follows.
Suppose X1 and X2 are two different numbers
with the same residue set, then
Therefore X1 and X2 are the Least Common
Multiple (LCM) of mi. But if the mi are
relatively prime, then their LCM is R, and it
must be that X1 and X2 is multiple of R. So it
cannot be that X1 < R and X2 < R. Therefore,
the set X m i: 1 ≤ i ≤ n is unique and may be
taken as the representation of X and such a
representation can be written in the form
x1 , x2 … xn where xi = X m i , and relationship
between X and its residues can be indicated by
writing X ≅ x1 , x2 … xn . The number R is
called the dynamic range of the RNS, because
the number of numbers that can be represented
is R.
II.WCDMA
One of the most promising approaches to 3G is
to combine a WCDMA air interface with the
fixed network of GSM without ignoring the
numerous advantages of the already existing
GSM networks. The standard that has emerged
is based on European Telecommunication
Standards Institute (ETSI) – UMTS and is
commonly known as UTRA [56, 57, 58, 59],
This air interface technology specified by 3rd
Generation Partnership Project (3GPP) applies
DS-CDMA technique for multiplexing different
users [13, 60, 61, 62, 63]. The information is
spread over a band of approximately 5 MHz.
Due to this wide bandwidth it called as
WCDMA i.e. Wideband CDMA. There are two
different modes of WCDMA –
Frequency Division Duplex(FDD) : The
uplink and downlink transmissions
employ two separated frequency bands
for this duplex method. A pair of
frequency bands with specified
separation is assigned for a connection.
│X1│mi =│X2│mi =) │X1 - X2│mi =
0 (2.1)
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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In this chapter all system description are
provided in FDD Mode.
Time Division Duplex (TDD) : In this
duplex method, uplink and downlink
transmission are carried over the same
frequency band by using synchronized
time intervals Thus time slots in
physical channel are divided into
transmission and reception part.
2.1.1 Physical Channel Structure
WCDMA defines two dedicated
physical channels in both links:
Dedicated Physical Data Channel
(DPDCH)
Dedicated Physical Control
Channel (DPDCH)
Each connection is allocated one DPCCH and
zero, one or many DPDCHs. In addition, there
are common physical channels defined as
Primary and secondary Common Physical
Channel (CCPCH), Synchronization Channel
(SCH) and Physical Random Access Channel
(PRACH)
Figure 4.1: Frame Structure for Uplink c DPDCH/DPCCH
Figure 2.1 shows the basic frame structure of
the uplink dedicated physical channels [61, 64,
65]. Each frame of 10 ms is split into 15 slot is
of the length Tslot= 0.666 ms with 2560 chips,
corresponding to one power control period. The
super frame length is 720 ms ; i.e. a super frame
corresponds to 72 frames. Pilot bits assists
coherent demodulation and channel estimation.
Transport Format Combination Indicator(TFCI)
is used to indicate and identify several
simultaneous services .Feedback Information
(FBI) bits are to be used to support techniques
requiring feedback. Transmit Power Control
(TPC) which stands for transmit power control
purposes. The Spreading Factor (SF) may range
from 256 down to 4. The spreading factor is
selected according to the date rate.
Above figure i.e. Figure 2.2 shows the basic
frame structure of the downlink dedicated
physical channels . As in the uplink, each frame
of 10 ms is split into 15 slots with a length of
2560 chips and 0.666ms duration. A super frame
corresponds to 720 ms, i.e. the super frame
Figure2.2: Frame Structure for Downlink DPCH
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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length corresponds to 72 frames. The spreading
factor thus has a range of 4 to 512. The different
control bits have similar meaning to those in the
uplink.
4.1.2 Spreading and Modulation
The basic modulation chip rate is 3.84 Mcps and
can be extended to 2×3.84 Mcps and 4×3.84
Mcps. The block diagram of uplink spreading
and modulation is shown in Figure 2.3. In the
uplink the data modulation of both the DPDCH
and the DPCCH is Binary Phase Shift Keying
(BPSK). The modulated DPCCH is mapped to
the Q-channel, while the first DPDCH is
mapped to I-channel. Subsequently added
DPDCHs are mapped alternatively to the I or the
Q-channel. Quaternary Phase Shift Keying
(QPSK) is applied for data modulation in the
downlink. Each pair of two bits are serial-to-
parallel converted and mapped to the I and Q
branches respectively. The data in I and Q
branches are spread to the chip rate by the same
channelization code. This spread signal is then
scrambled by a cell specific scrambling code.
Fig 2.3 a cell specific scrambling code.
Figure 2.4 shows the spreading and modulation for a downlink user. Spreading modulation consists of
two different operations. The first one is spreading where each data symbol is spread to the signal. The
second operation is scrambling where a complex valued scrambling code is applied to spread signal.
fig4
fig 2.4. a cell specific channelization code.
Channelization Code
OVSF codes are used for channelization. All the
codes within the code tree cannot be used
simultaneously by a mobile station. A code can
be used by an MS if and only if no other code on
the path from specific code to the root of the tree
or in the sub-tree below the specific code is used
by the same MS. Uplink channelization code
may be allocated if more than one uplink
DPDCH is required whereas different physical
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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channels use different channelization code in
downlink.
Scrambling Code
The scrambling codes are designed so that has
very low cross-correlation among them. This
ensures good Multiple Access Interference
(MAI) rejection capability. Either short or long
scrambling codes can be used in the uplink.
Short scrambling codes are recommended for
base stations equipped with advanced receivers
employing multiuser detection or interference
cancellation. Long scrambling codes are used
since a simple rake receiver is employed in the
simulator design. These are Gold codes
generated from the position wise modulo 2 sum
of two binary m-sequence.
III. RNS Based PN Sequence
Generator
In most communication systems,
spreading codes or sequences can be
generated in an off-line way and is saved
in a look-up table, which can be called
whenever needed. Similarly RNS based
PN sequence generation [27] also consists
of an off-line process for the generation
of Initial Primal Vector and finally the
generation of the required PN sequence
from the stored primal vectors which is
done on-line. The off-line process is
summarized in Fig 3.5. The external
inputs to these blocks include spreading
factor, and the Cross Correlation
Threshold (CF). Module selection is used
here. Table 3.1 shows the generated
module set and dynamic range, R for
various spreading factors using
Consecutive module selection method.
For a given spread factor, the number of
users that can be accommodated is huge
in comparison to other spreading codes.
A primal, J1 is randomly selected from
the range, R in eq. 2.10.The
corresponding residue set, Rs(J1) is the
output of Decimal to Residue Arithmetic
Converter. The generated residue
numbers are concatenated and converted
into 8 bit (since k=8) binary sequence of
1 and 0. This sequence is passed through
the NRZ encoder to get the sequence c1
corresponding to primal J1. This
procedure is repeated for every primal in
range, R. The generated sequences are
tested for correlation amongst themselves
such that
Correlation between ci and cj, i=j has to
be unity.
Correlation between ci and cj, i≠j has to
preferably less than a threshold T. This
threshold can vary for different
applications based on the channel
properties and error tolerance.
The primal which satisfies this criteria
forms the Primal Pool, J. Consider an
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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example for the proposed PN Sequence
Generation for β=16, M=[255 254] and
CF = 0.25. Table 3.2 shows the generated
the PN Sequence for the randomly
selected primals. These sequences are
then tested for correlation among
themselves which is listed in Table 3.3.
Since the defined system requires a
threshold of 0.25, discard J5 and add J1 ,
J2, J3 , J4 to the final primal pool, J.
𝑅𝑠 𝐽1 = 𝐽1 𝑝1, 𝐽1 𝑝2
, … 𝐽1 𝑝𝑚 (3.4)
Figure 3.5: Offline process for RNS Based PN Sequence Generation
Figure 3.5: Offline process for RNS Based PN Sequence Generation
The next phase, shown in figure 3.6,
starts when the system under
consideration demands for signature
waveforms. Depending upon the
application and number of users active in
the system, the primal vector, J
𝐽
= 𝐽1, 𝐽2 , 𝐽3, …𝐽𝑈 𝑇 (3.5)
is selected from the Primal Pool with
spread factor, along with number of
active users, U as input. The residue
matrix 𝑅𝑠 = 𝐽 𝑀 is created in RNS
converter block such that Rs =[Rs(J1),
Rs(J2), Rs(J3),…Rs(JU )]. Finally the
required RNS based PN code matrix, c =
[c1, c2…cU] of size U X β is formed after
binary conversion and encoding. The
maximum size of the proposed code set is
very large with respect to other PN
sequences. This offers the provision to
vary correlation threshold based on the
channel properties and error threshold of
the system under consideration.
Table 3.2: RNS Based PN Sequence
Generation
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Primal, J PN Sequence
Based on RNS, c
1 -1 -1 -1 -1 -
1 -1 -1 1 -1 -1 -1 -1 -
1 -1 -1
321 -1 1 -1 -1 -1 -
1 1 -1 -1 1 -1 -1 -1 -1 1 1
550 -1 -1 1 -1 1 -
1 -1 -1 -1 -1 1 -1 1 -1 1 -1
2356 -1 -1 1 1 1 -
1 1 -1 1 -1 -1 -1 1 1 -1 1
64000 1 1 1 1 1 -1 1 -1
1 1 1 1 -1 1 1 -1
Primals are selected within the Range, R
R = 255X254 = 64770
a. DS-CDMA System Model
Consider a mobile receiver for CDMA
with U simultaneous transmission plus
Additive White Gaussian Noise (AWGN)
as shown in Figure 3.7. The transmitted
signal at time t is constructed by
summing the spread sequence of each
user.The noise corrupted received signal
y(t) is defined- 𝑦 𝑡 = 𝑥 𝑡 +
𝜂 𝑡 (3.6)
Where η(t) denotes the white Gaussian
noise. The uth
users transmitted data bit
for bit k is denoted ad du(k) and is either
+1 or -1 with equal probability and all
users are transmitting with equal power,
normalized to one. Then, the received
signal x(t) due to the uth
user is given by:
𝑥𝑢 𝑡 = 2𝑃𝑢
𝑈
𝑢=1
𝑑𝑢(𝑘)
∞
𝑘=−∞
𝑠𝑢 𝑡 − 𝑘𝑇𝑏
− 𝑇𝑢 𝑐𝑜𝑠 𝜔𝑐𝑡
+ 𝜙𝑢 (3.7)
Table 3.3: Correlation Matrix of the
Generated Sequence
Where 𝑃𝑢 , 𝑇𝑢 , and φ𝑢
are the power,
delay, and carrier phase shift of the Uth
user, and ωc is the carrier frequency ;
Su(t) is the uth
spreading (signature)
waveform given by
𝑠𝑢 𝑡
= 𝑐𝑢 ,𝑛
𝐿−1
𝑛=0
𝜑 𝑡
= 𝑛𝑇𝑐 (3.8)
Where 𝑐𝑢 ,𝑛𝜖 1, −1 is the nth
element of
the spreading sequence for user u, φ(t) is
the chip waveform and L the spreading
sequence length. In order to simplify the
C1 C2 C3 C4 C5
C1 1 0.15 -0.25 0 -0.65
C2 0.1 1 -0.16 -0.13 0.07
C3
-
0.2 -0.16 1 0.13 0.07
C4 0 -0.13 0.13 1 0
C5
-
0.6 0.07 0.07 0 1
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notation, it is assumed that all carrier
phases are equal to zero and baseband
notation can be used [47]. Since the
signal processing task is done on sampled
signals, it is more convenient to make use
of vector and matrix notation. Therefore
Equation 3.6 can be rewritten for a fully
synchronized downlink antipodal {+1,-1}
DS-CDMA system with U independent
users and a non-dispersive AWGN
channel.
𝑘𝐿 + 𝑛 = 𝑑𝑢(𝑘)𝑐𝑢 ,𝑛
𝑈
𝑢=1
+ 𝜂 𝑘𝐿 + 𝑛 (3.9)
The received signal becomes y(k) in vector notation, where k denotes the kth
user bit. If the
signal is transmitted through a channel with ISI, then equation 3.6 becomes
𝑦 = 𝑘𝐿 + 𝑛 = 𝐻 𝑧 ⊗ 𝑥 𝑘𝐿 + 𝑛 + 𝜂 𝑘𝐿 + 𝑛 (3.10)
Where ⨂ represents convolution
operation and H(z) is channel impulse
response [54]. A CDMA receiver
processes the received signal with either a
bank of matched filters (MFs) or RAKEs.
To recover the data, the received signal is
multiplied by the required sequence,
which is generated locally by the
receiver. For a multipath scenario, the
spreading codes ci where i=1 to U is
replaced by the convolution between
𝐶𝑖⨂𝐻𝑐ℎ RNS based PN sequences are
used as spreading sequence for the
system under consideration.
b. Comparison of RNS based PN
sequence with other CDMA codes
A comparison in terms of number of
codes in the code set and correlation
Figure 3.7 Block Diagram of DS-CDMA System
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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properties is made for the proposed
sequence with respect to other CDMA
codes that are used in various mobile
cells.
3.4 Number of Sequences
Table 3.4 shows the comparison of
number of available codes for cell for the
proposed sequence with other CDMA
codes for a given spreading factor. N
length Walsh-Hadamard (WH) sequence
are derived from Walsh-Hadamard matrix
of size N×N to support N different users
[52]. For a particular sequence length, the
OVSF codes are basically the same as
WH sequences. The only difference
between the two is that the latter allow
combinational use of WH sequences with
different length [53].This creates Code
Assignment Blocking problem thus
limiting the number of users close to one
fifth of the maximal spreading factor [1].
An n-stage shift register can generate a
maximal spreading factor [1]. An n-stage
shift register can generate a maximal
length sequence of 2n-1 bits [52].Shifted
combinations of this sequence gives
N=2n-1 number of sequences. Gold
Sequence is constructed by modulo-2
addition of two m-sequences of the same
length with each other [51]. Including the
two m-sequences used for addition a total
of N+1 sequence are formed.
The data in Table 3.4 shows that the
number of sequences from the proposed
PN Sequence Generator with the module
set in Table 3.1 is very huge. This range
can also be altered by changing the
module set.
IV. Correlation Properties
For comparing cross-correlation
properties with other standard PN
sequence, the proposed PN sequence are
generated for β= 8 and module set P=
[255].
The primal vector, J=[10 39 60 77 86 25
140], is generated varying the threshold
value from 0 to 0.25. The correlation
matrix of RNS based PN sequence; Gold
sequence and Maximal Length sequence
are tabulated in Table 3.5, Table 3.6 and
Table 3.7 respectively. The data shows
that the maximum cross correlation
between any two sequences is limited to
0.25 for RNS based PN sequence whereas
it come up to 0.41 and 0.73 for gold
sequences, while the auto correlation
reaches to 1.
International Journal of Computer Architecture and Mobility (ISSN 2319-9229) Volume 3 -Issue 1A, February 2015
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Table 3.4: Length of the code set for different CDMA Codes
Table
3.5:
Correlation Matrix for RNS based PN Sequence, = 8
Orthogonal Code Pseudo Random Sequence
WH OVSF
M Gold RNS based
code code sequence sequence sequence
8 8 8 7 9 255
16 16 16 15 17 64770
32 32 32 31 33 411308931
128 128 128 127 129
10^19
= 1040
PN1 PN2 PN3 PN4 PN5 PN6 PN7
PN1 1 0 0 0 0 0.14 0.14
PN2 0 1 0 0 0 -0.2 -0.2
PN3 0 0 1 0
0 0.2 0.2
PN4 0 0 0 1 0 0.2 0.2
PN5 0 0 0 0 1 -0.2 -0.2
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Table3.6 Correlation Matrix for Gold Sequence, β = 8
V.
VI.
VII.
VIII.
Conclusion
The core of the next generation
CDMA technology lies in CDMA
code design approach which should
take into account as many real
operational conditions as possible and
to maintain a sufficiently large code
set size. In this context, this thesis
work contributed a little towards the
evolution of next generation CDMA
technology because the generated PN
sequence based on Residue
arithmetic:
Offers MAI-resistant
operation for DS-CDMA
systems in both synchronous
and asynchronous MAI-
AWGN channels, reducing
co-channel interference and
increasing capacity in a
mobile cellular system. The
joint effect of ideal auto-
correlation functions and good
cross correlation function
PN6 0.1 -0.2 0.2 0.2 -0.2 1 -0.0
PN7 0.1 -0.2 0.2 0.2 -0.2 -.06 1
PN1 PN2 PN3 PN4 PN5 PN6 PN7
PN1 1 0.41 -.09 -0.1 -.09 -.09 -.35
PN2 0.41 1 -.09 0.4 .09 -.09 -.35
PN3 -.09 -.09 1 -.09 -.40 -.40 0.25
PN4 -.16 0.41 -.09 1 -.09 -.09 -.35
PN5 -.09 -.09 -.40 -.09 1 -.40 .25
PN6 -.09 -.09 -.40 -.09 -.40 1 0.25
PN7 -.35 -.35 0.25 -.35 0.25 0.25 1
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makes RNS based PN
sequence superior to all other
standard PN sequence like
Gold codes, Kasami codes and
Maximal Length sequence
Offers provision to vary
correlation threshold based on
the channel properties and
error tolerance thus providing
real operational conditions for
spreading code design unlike
any existing techniques.
Inherits high dynamic key
range to maintain large code
sets such that large number of
users can be accommodated.
In multipath AWGN, Ricean
Fading and Rayleigh Fading
environments, the generated
PN sequence outperforms the
existing Walsh Hadamard
code as channelization code
for downlink WCDMA
system. Thus the obtained
spreading sequences can
inherently address MAI in a
multi-user system and MI
imultipath environment
without using other external
auxiliary subsystems to
overcome those impairments.
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